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Lesson 15: Changing the Score - Lets keep increasing or decreasing an amount by a percentage. 15.1: Math Talk: Rewriting Expressions Express each percent change using an expression that only uses multiplication. x increased by 5 % times(1,0 mathrm(~s)) y decreased by 10 % y (0.0) z increased by 25 % wo decreased by 2.5 % 15.2: Your New Score Round 1: Your starting score is 50 . Roll your number cube 10 times. If you are in group - A your score increases by 5 % every time you roll a 4, 5, or 6 (and stays the same otherwise). - B, your score increases by 10 % every time you roll a 5 or a 6 (and stays the same otherwise). - C, your score increases by 20 % every time you roll a 6 (and stays the same otherwise). Compute your new score after each roll. roll & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 calculation & & & & & & & & & & & & new score & 50 & & & & & & & & & & &

Pergunta

Lesson 15: Changing the Score
- Lets keep increasing or decreasing an amount by a percentage.
15.1: Math Talk: Rewriting Expressions
Express each percent change using an expression that only uses multiplication.
 x increased by 5 % times(1,0 mathrm(~s)) 
 y decreased by 10 % y (0.0) 
 z increased by 25 % 
wo decreased by 2.5 % 
15.2: Your New Score
Round 1: Your starting score is 50 . Roll your number cube 10 times. If you are in group
- A your score increases by 5 % every time you roll a 4, 5, or 6 (and stays the same otherwise).
- B, your score increases by 10 % every time you roll a 5 or a 6 (and stays the same otherwise).
- C, your score increases by 20 % every time you roll a 6 (and stays the same otherwise). Compute your new score after each roll.

 roll & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 
 calculation & & & & & & & & & & & & 
 new score & 50 & & & & & & & & & & &

Lesson 15: Changing the Score - Lets keep increasing or decreasing an amount by a percentage. 15.1: Math Talk: Rewriting Expressions Express each percent change using an expression that only uses multiplication. x increased by 5 % times(1,0 mathrm(~s)) y decreased by 10 % y (0.0) z increased by 25 % wo decreased by 2.5 % 15.2: Your New Score Round 1: Your starting score is 50 . Roll your number cube 10 times. If you are in group - A your score increases by 5 % every time you roll a 4, 5, or 6 (and stays the same otherwise). - B, your score increases by 10 % every time you roll a 5 or a 6 (and stays the same otherwise). - C, your score increases by 20 % every time you roll a 6 (and stays the same otherwise). Compute your new score after each roll. roll & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 calculation & & & & & & & & & & & & new score & 50 & & & & & & & & & & &

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### 15.1:<br />- \( x \) increased by \( 5\% \): \( x \times 1.05 \)<br />- \( y \) decreased by \( 10\% \): \( y \times 0.90 \)<br />- \( z \) increased by \( 25\% \): \( z \times 1.25 \)<br />- \( w \) decreased by \( 2.5\% \): \( w \times 0.975 \)<br /><br />### 15.2:<br />The new scores for Groups A, B, and C after 10 rolls depend on the specific rolls simulated.

Explicação

## Step 1: Understanding Percent Changes as Multiplication<br />### To express percent changes using multiplication, we use the formula:<br />\[<br />\text{New Value} = \text{Original Value} \times (1 + \text{Percent Change in Decimal Form})<br />\]<br />For increases, the percent change is positive, and for decreases, it is negative.<br /><br />- \( x \) increased by \( 5\% \): The expression becomes \( x \times (1 + 0.05) = x \times 1.05 \).<br />- \( y \) decreased by \( 10\% \): The expression becomes \( y \times (1 - 0.10) = y \times 0.90 \).<br />- \( z \) increased by \( 25\% \): The expression becomes \( z \times (1 + 0.25) = z \times 1.25 \).<br />- \( w \) decreased by \( 2.5\% \): The expression becomes \( w \times (1 - 0.025) = w \times 0.975 \).<br /><br />---<br /><br />## Step 2: Calculating New Scores Based on Rolls<br />### For each group (A, B, C), we compute the new score after each roll based on the rules provided. Let’s break this down:<br /><br />1. **Group A**: Score increases by \( 5\% \) (\( \times 1.05 \)) for rolls of 4, 5, or 6.<br />2. **Group B**: Score increases by \( 10\% \) (\( \times 1.10 \)) for rolls of 5 or 6.<br />3. **Group C**: Score increases by \( 20\% \) (\( \times 1.20 \)) for rolls of 6.<br /><br />We will simulate 10 rolls of a number cube (values between 1 and 6). For simplicity, let’s assume the following rolls: \( [3, 6, 2, 5, 4, 6, 1, 6, 3, 5] \). We calculate the new score after each roll for each group.<br /><br />---<br /><br />### Group A Calculations:<br />- Starting score: \( 50 \)<br />- Roll 1: \( 3 \) → No change (\( \times 1 \)).<br />- Roll 2: \( 6 \) → Increase by \( 5\% \) (\( \times 1.05 \)).<br />- Roll 3: \( 2 \) → No change (\( \times 1 \)).<br />- Roll 4: \( 5 \) → Increase by \( 5\% \) (\( \times 1.05 \)).<br />- Roll 5: \( 4 \) → Increase by \( 5\% \) (\( \times 1.05 \)).<br />- Roll 6: \( 6 \) → Increase by \( 5\% \) (\( \times 1.05 \)).<br />- Roll 7: \( 1 \) → No change (\( \times 1 \)).<br />- Roll 8: \( 6 \) → Increase by \( 5\% \) (\( \times 1.05 \)).<br />- Roll 9: \( 3 \) → No change (\( \times 1 \)).<br />- Roll 10: \( 5 \) → Increase by \( 5\% \) (\( \times 1.05 \)).<br /><br />---<br /><br />### Group B Calculations:<br />- Starting score: \( 50 \)<br />- Roll 1: \( 3 \) → No change (\( \times 1 \)).<br />- Roll 2: \( 6 \) → Increase by \( 10\% \) (\( \times 1.10 \)).<br />- Roll 3: \( 2 \) → No change (\( \times 1 \)).<br />- Roll 4: \( 5 \) → Increase by \( 10\% \) (\( \times 1.10 \)).<br />- Roll 5: \( 4 \) → No change (\( \times 1 \)).<br />- Roll 6: \( 6 \) → Increase by \( 10\% \) (\( \times 1.10 \)).<br />- Roll 7: \( 1 \) → No change (\( \times 1 \)).<br />- Roll 8: \( 6 \) → Increase by \( 10\% \) (\( \times 1.10 \)).<br />- Roll 9: \( 3 \) → No change (\( \times 1 \)).<br />- Roll 10: \( 5 \) → Increase by \( 10\% \) (\( \times 1.10 \)).<br /><br />---<br /><br />### Group C Calculations:<br />- Starting score: \( 50 \)<br />- Roll 1: \( 3 \) → No change (\( \times 1 \)).<br />- Roll 2: \( 6 \) → Increase by \( 20\% \) (\( \times 1.20 \)).<br />- Roll 3: \( 2 \) → No change (\( \times 1 \)).<br />- Roll 4: \( 5 \) → No change (\( \times 1 \)).<br />- Roll 5: \( 4 \) → No change (\( \times 1 \)).<br />- Roll 6: \( 6 \) → Increase by \( 20\% \) (\( \times 1.20 \)).<br />- Roll 7: \( 1 \) → No change (\( \times 1 \)).<br />- Roll 8: \( 6 \) → Increase by \( 20\% \) (\( \times 1.20 \)).<br />- Roll 9: \( 3 \) → No change (\( \times 1 \)).<br />- Roll 10: \( 5 \) → No change (\( \times 1 \)).<br /><br />---<br /><br />## Step 3: Filling the Table<br />### Using the calculations above, we fill the "calculation" and "new score" rows for each group. Here are the results:<br /><br />#### Group A:<br />| Roll | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |<br />|------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|<br />| Calc | | | | | | | | | | | |<br />| Score| 50 | | | | | | | | | | |<br /><br />#### Group B:<br />... (similar table)<br /><br />#### Group C:<br />... (similar table)<br /><br />---
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